Convert each radian measure to degrees. See Examples 2(a) and 2(b). 7π/4

검증된 단계별 안내

Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).

Substitute the given radian measure \(\frac{7\pi}{4}\) into the formula: \(\text{Degrees} = \frac{7\pi}{4} \times \frac{180}{\pi}\).

Simplify the expression by canceling out \(\pi\) in the numerator and denominator: \(\text{Degrees} = \frac{7}{4} \times 180\).

Multiply the fraction by 180: \(\text{Degrees} = \frac{7 \times 180}{4}\).

Simplify the fraction to find the degree measure.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Radian Measure

A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry, where 2π radians equal 360 degrees.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a full rotation, making it intuitive for everyday use and angle measurement.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian value by 180/π. This ratio comes from the equivalence of 2π radians to 360 degrees. For example, 7π/4 radians equals (7π/4) × (180/π) = 315 degrees.